zla_gbamv - vector operation to calculate error bounds
SUBROUTINE ZLA_GBAMV(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY) DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS DOUBLE COMPLEX AB(LDAB,*), X(*) DOUBLE PRECISION Y(*) SUBROUTINE ZLA_GBAMV_64(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY) DOUBLE PRECISION ALPHA, BETA INTEGER*8 INCX, INCY, LDAB, M, N, KL, KU, TRANS DOUBLE COMPLEX AB(LDAB,*), X(*) DOUBLE PRECISION Y(*) F95 INTERFACE SUBROUTINE LA_GBAMV(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY) INTEGER :: TRANS, M, N, KL, KU, LDAB, INCX, INCY REAL(8), DIMENSION(:) :: Y COMPLEX(8), DIMENSION(:,:) :: AB COMPLEX(8), DIMENSION(:) :: X REAL(8) :: ALPHA, BETA SUBROUTINE LA_GBAMV_64(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY) INTEGER(8) :: TRANS, M, N, KL, KU, LDAB, INCX, INCY REAL(8), DIMENSION(:) :: Y COMPLEX(8), DIMENSION(:,:) :: AB COMPLEX(8), DIMENSION(:) :: X REAL(8) :: ALPHA, BETA C INTERFACE #include <sunperf.h> void zla_gbamv (int trans, int m, int n, int kl, int ku, double alpha, doublecomplex *ab, int ldab, doublecomplex *x, int incx, dou- ble beta, double *y, int incy); void zla_gbamv_64 (long trans, long m, long n, long kl, long ku, double alpha, doublecomplex *ab, long ldab, doublecomplex *x, long incx, double beta, double *y, long incy);
Oracle Solaris Studio Performance Library zla_gbamv(3P)
NAME
zla_gbamv - perform a matrix-vector operation to calculate error bounds
SYNOPSIS
SUBROUTINE ZLA_GBAMV(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX,
BETA, Y, INCY)
DOUBLE PRECISION ALPHA, BETA
INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
DOUBLE COMPLEX AB(LDAB,*), X(*)
DOUBLE PRECISION Y(*)
SUBROUTINE ZLA_GBAMV_64(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX,
BETA, Y, INCY)
DOUBLE PRECISION ALPHA, BETA
INTEGER*8 INCX, INCY, LDAB, M, N, KL, KU, TRANS
DOUBLE COMPLEX AB(LDAB,*), X(*)
DOUBLE PRECISION Y(*)
F95 INTERFACE
SUBROUTINE LA_GBAMV(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX,
BETA, Y, INCY)
INTEGER :: TRANS, M, N, KL, KU, LDAB, INCX, INCY
REAL(8), DIMENSION(:) :: Y
COMPLEX(8), DIMENSION(:,:) :: AB
COMPLEX(8), DIMENSION(:) :: X
REAL(8) :: ALPHA, BETA
SUBROUTINE LA_GBAMV_64(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX,
BETA, Y, INCY)
INTEGER(8) :: TRANS, M, N, KL, KU, LDAB, INCX, INCY
REAL(8), DIMENSION(:) :: Y
COMPLEX(8), DIMENSION(:,:) :: AB
COMPLEX(8), DIMENSION(:) :: X
REAL(8) :: ALPHA, BETA
C INTERFACE
#include <sunperf.h>
void zla_gbamv (int trans, int m, int n, int kl, int ku, double alpha,
doublecomplex *ab, int ldab, doublecomplex *x, int incx, dou-
ble beta, double *y, int incy);
void zla_gbamv_64 (long trans, long m, long n, long kl, long ku, double
alpha, doublecomplex *ab, long ldab, doublecomplex *x, long
incx, double beta, double *y, long incy);
PURPOSE
zla_gbamv performs one of the matrix-vector operations
y := alpha*abs(A)*abs(x) + beta*abs(y), or y :=
alpha*abs(A)**T*abs(x) + beta*abs(y),
where alpha and beta are scalars, x and y are vectors and A is an m by
n matrix.
This function is primarily used in calculating error bounds. To pro-
tect against underflow during evaluation, components in the resulting
vector are perturbed away from zero by (N+1) times the underflow
threshold. To prevent unnecessarily large errors for block-structure
embedded in general matrices, "symbolically" zero components are not
perturbed. A zero entry is considered "symbolic" if all multiplica-
tions involved in computing that entry have at least one zero multipli-
cand.
ARGUMENTS
TRANS (input)
TRANS is INTEGER
On entry, TRANS specifies the operation to be performed as
follows:
BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)
BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
Unchanged on exit.
M (input)
M is INTEGER
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N (input)
N is INTEGER
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
KL (input)
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input)
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
ALPHA (input)
ALPHA is DOUBLE PRECISION
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
AB (input)
AB is COMPLEX*16 array of DIMENSION ( LDAB, n )
Before entry, the leading m by n part of the array AB must
contain the matrix of coefficients.
Unchanged on exit.
LDAB (input)
LDAB is INTEGER
On entry, LDAB specifies the first dimension of AB as
declared in the calling (sub) program. LDAB must be at least
max( 1, m ).
Unchanged on exit.
X (input)
X is COMPLEX*16 array, dimension
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the vector
x.
Unchanged on exit.
INCX (input)
INCX is INTEGER
On entry, INCX specifies the increment for the elements of X.
INCX must not be zero.
Unchanged on exit.
BETA (input)
BETA is DOUBLE PRECISION
On entry, BETA specifies the scalar beta. When BETA is sup-
plied as zero then Y need not be set on input.
Unchanged on exit.
Y (input/output)
Y is DOUBLE PRECISION array, dimension
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry with BETA non-zero, the incremented array Y must
contain the vector y. On exit, Y is overwritten by the
updated vector y.
INCY (input)
INCY is INTEGER
On entry, INCY specifies the increment for the elements of Y.
INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.
7 Nov 2015 zla_gbamv(3P)